As you know, the molecules and atoms that make up the objects around us are very small. To carry out calculations during chemical reactions, as well as to analyze the behavior of a mixture of non-interacting components in liquids and gases, the concept of mole fractions is used. What they are, and how they can be used to obtain the macroscopic physical quantities of a mixture, is discussed in this article.
Avogadro's number
At the beginning of the 20th century, while conducting experiments with gas mixtures, the French scientist Jean Perrin measured the number of H2 molecules contained in 1 gram of this gas. This number turned out to be a huge number (6,0221023). Since it is extremely inconvenient to carry out calculations with such figures, Perrin proposed a name for this value - Avogadro's number. This name was chosen in honor of the Italian scientist of the early 19th century, Amedeo Avogadro, who, like Perrin, studied mixtures of gases and was even able to formulatefor them, the law that currently bears his last name.
Avogadro's number is currently widely used in the study of various substances. It links macroscopic and microscopic characteristics.
Amount of substance and molar mass
In the 60s, the International Chamber of Weights and Measures introduced the seventh basic unit of measurement into the system of physical units (SI). It became a moth. The mole shows the number of elements that make up the system in question. One mole is equal to Avogadro's number.
Molar mass is the weight of one mole of a given substance. It is measured in grams per mole. The molar mass is an additive quantity, that is, to determine it for a particular chemical compound, it is necessary to add the molar masses of the chemical elements that make up this compound. For example, the molar mass of methane (CH4) is:
MCH4=MC + 4MH=12 + 41=16 g/mol.
That is, 1 mole of methane molecules will have a mass of 16 grams.
Mole fraction concept
Pure substances are rare in nature. For example, various impurities (s alts) are always dissolved in water; The air of our planet is a mixture of gases. In other words, any substance in the liquid and gaseous state is a mixture of various elements. The mole fraction is a value showing what part in mole equivalent is occupied by one or another component inmixtures. If the amount of the substance of the whole mixture is denoted as n, and the amount of the substance of component i is denoted as ni, then the following equation can be written:
xi=ni / n.
Here xi is the mole fraction of component i for this mixture. As can be seen, this quantity is dimensionless. For all components of the mixture, the sum of their mole fractions is expressed by the formula as follows:
∑i(xi)=1.
Getting this formula is not difficult. To do this, just substitute the previous expression for xi.
into it
Atomic interest
When solving problems in chemistry, often the initial values are given in atomic percent. For example, in a mixture of oxygen and hydrogen, the latter is 60 atomic%. This means that out of 10 molecules in the mixture, 6 will correspond to hydrogen. Since the mole fraction is the ratio of the number of component atoms to their total number, atomic percentages are synonymous with the concept in question.
The conversion of shares into atomic percentages is carried out by simply increasing them by two orders of magnitude. For example, 0.21 mole fraction of oxygen in air corresponds to 21 atomic%.
Ideal gas
The concept of mole fractions is often used in solving problems with gas mixtures. Most gases under normal conditions (temperature 300 K and pressure 1 atm.) Are ideal. This means that the atoms and molecules that make up the gas are at a great distance from each other and do not interact with each other.
For ideal gases, the following equation of state is valid:
PV=nRT.
Here P, V and T are three macroscopic thermodynamic characteristics: pressure, volume and temperature respectively. The value R=8, 314 J / (Kmol) is a constant for all gases, n is the number of particles in moles, that is, the amount of substance.
The equation of state shows how one of the three macroscopic gas characteristics (P, V or T) will change if the second of them is fixed and the third is changed. For example, at a constant temperature, the pressure will be inversely proportional to the volume of the gas (Boyle-Mariotte law).
The most remarkable thing about the written formula is that it does not take into account the chemical nature of the molecules and atoms of the gas, that is, it is valid for both pure gases and their mixtures.
D alton's Law and partial pressure
How to calculate the mole fraction of a gas in a mixture? To do this, it is sufficient to know the total number of particles and their number for the component under consideration. However, you can do otherwise.
The mole fraction of a gas in a mixture can be found by knowing its partial pressure. The latter is understood as the pressure that a given component of the gas mixture would create if it were possible to remove all other components. If we designate the partial pressure of the i-th component as Pi, and the pressure of the entire mixture as P, then the mole fraction formula for this component will take the form:
xi=Pi / P.
Because the amountof all xi is equal to one, then we can write the following expression:
∑i(Pi / P)=1, hence ∑i (Pi)=P.
The last equality is called D alton's law, which is so named after the British scientist of the early 19th century, John D alton.
The law of partial pressure or D alton's law is a direct consequence of the equation of state for ideal gases. If atoms or molecules in a gas begin to interact with each other (this happens at high temperatures and high pressure), then D alton's law is unfair. In the latter case, to calculate the mole fractions of the components, it is necessary to use the formula in terms of the amount of substance, and not in terms of partial pressure.
Air as a gas mixture
Having considered the question of how to find the mole fraction of a component in a mixture, we solve the following problem: calculate the values xi and Pi for each component in air.
If we consider dry air, then it includes the following 4 gas components:
- nitrogen (78.09%);
- oxygen (20.95%);
- argon (0.93%);
- carbon dioxide gas (0.04%).
From this data, the mole fractions for each gas are very easy to calculate. To do this, it is enough to present the percentages in relative terms, as mentioned above in the article. Then we get:
xN2=0, 7809;
xO2=0, 2095;
xAr=0, 0093;
xCO2=0, 0004.
Partial pressurewe calculate these air components, given that the atmospheric pressure at sea level is 101 325 Pa or 1 atm. Then we get:
PN2=xN2 P=0.7809 atm.;
PO2=xO2 P=0, 2095 atm.;
PAr=xAr P=0.0093 atm.;
PCO2=xCO2 P=0.0004 atm.
This data means that if you remove all oxygen and other gases from the atmosphere, and leave only nitrogen, the pressure will drop by 22%.
Knowing the partial pressure of oxygen plays a vital role for people who dive underwater. So, if it is less than 0.16 atm., then the person instantly loses consciousness. On the contrary, the partial pressure of oxygen exceeds the mark of 1.6 atm. leads to poisoning with this gas, which is accompanied by convulsions. Thus, a safe partial pressure of oxygen for human life should lie within 0.16 - 1.6 atm.
